Permutation and Multi-permutation Codes Correcting Multiple Deletions
Shuche Wang, The Nguyen, Yeow Meng Chee, Van Khu Vu

TL;DR
This paper advances permutation codes in the Ulam metric by improving bounds, designing efficient decoding algorithms for multiple deletions, and establishing new mappings connecting permutation codes across different metrics.
Contribution
It introduces a new mapping linking permutation codes in Hamming and Ulam metrics, improves bounds on code size, and constructs codes correcting multiple deletions and bursts with efficient decoding.
Findings
Improved Gilbert--Varshamov bound for permutation codes
Designed permutation codes correcting multiple deletions with low redundancy
Constructed best-known multi-permutation codes in Ulam metric
Abstract
Permutation codes in the Ulam metric, which can correct multiple deletions, have been investigated extensively recently. In this work, we are interested in the maximum size of permutation codes in the Ulam metric and aim to design permutation codes that can correct multiple deletions with efficient decoding algorithms. We first present an improvement on the Gilbert--Varshamov bound of the maximum size of these permutation codes by analyzing the independence number of the auxiliary graph. The idea is widely used in various cases and our contribution in this section is enumerating the number of triangles in the auxiliary graph and showing that it is small enough. Next, we design permutation codes correcting multiple deletions with a decoding algorithm. In particular, the constructed permutation codes can correct deletions with at most bits of redundancy where…
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Taxonomy
TopicsCoding theory and cryptography · graph theory and CDMA systems · Error Correcting Code Techniques
